Aren't they capable of taking an external mains to DC power in feed?
My Sony worldband is similar lives on mains unless I am travelling. It does last pretty well on batteries too - more than a week.
And also eats batteries like there is no tomorrow.
That is a problem with things that are tetchy about min battery voltage.
You best bet is find a wall wart supply either official or unofficial. You will need to pay careful attention to polarity. Several fan sites for Grundig radios should have relevant model details.
Maplin do something like you would need.
Better prices available elsewhere if you know exactly what you want.